The Leave to Remain is the legal status of a person issued by a government office of internal affairs to one who is not yet a citizen. In most stable countries, Indefinite leave to remain (as is known in the UK) is granted to these foreign citizens after a specified period spent within its borders. Indefinite leave to remain ( ILR) is an immigration status granted to a person who does not hold right of abode in the United Kingdom, but who has been admitted This is usually the final step towards naturalization which in turn leads to full citizenship. Naturalization is the acquisition of Citizenship or Nationality by somebody who was not a citizen or national of that country when he or she was born
A Leave to Remain need not be indefinite.
Compare to Permanent Resident status in the United States and Permanent Resident (used to known as Landed Immigrant) status in Canada.